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The Puzzling Negative Orbit-Period Derivative of the Low-Mass X-Ray Binary 4U 1820-30 in NGC 6624

4U 1820-30 is a low-mass X-ray binary near the center of the globular cluster NGC 6624 consisting of, at least, one neutron star and one helium white dwarf. Analyzing 16 years of data from the Rossi X-ray Timing Explorer (RXTE) allows us to measure its orbital period and its time derivative with unprecedented accuracy to be P = 685.01197 +- 0.00003 s and dP/dt /P = -5.3 +- 0.3x10^-8 yr^-1. Hence, we confirm that the period derivative is significantly negative at the >17 sigma level, contrary to theoretical expectations for an isolated X-ray binary. We discuss possible scenarios that could explain this discrepancy, and conclude that the center of NGC 6624 most likely contains large amounts of non-luminous matter such as dark remnants. We also discuss the possibility of an IMBH inside NGC 6624, or that a dark remnant close to 4U 1820-30 causes the observed shift.